The present invention relates to a new and distinct hybrid of Agastache plant named ‘Velvet Crush’ characterized by the combination of taller purple stems, darker green foliage; light pink flowers, and rose color calyxes on 80 cm plants compared to the seed parent. The new Agastache hybrid was raised as a seedling from open pollinated seed sown from the seed parent Agastache cana ‘Bolero’, not patented, in Hebron, Ill. in 2015. The selection of the new plant was due to its' taller purple stems, light pink flowers, and rose colored calyxes compared to the seed parent. Initial asexual reproduction has taken place at a nursery in Hebron, Ill. since 2016 by means of vegetative cuttings. The new Agastache hybrid has shown to be stable and identical in reproduction to the initially discovered plant after rooting over 300 plants from 2015 to 2016. No plants of the new Monarda have been sold in this country, or anywhere in the world, prior to the filing of this application, nor has any disclosure of the new plant been made prior to the filing of this application with the exception of that which was disclosed within one year of filing of this application and was either derived directly or indirectly for the inventor.